The concept "golden ratio" has two senses — mathematical and esthetic. They are closely connected among themselves. The esthetic meaning of golden ratio is that the strongest impression on the viewer is rendered by objects of art with a harmonious ratio whole and parts. The mathematics attaches to this ratio numerical significance. Still antique sculptors and architects used the rule of golden ratio. Calculations are attributed to Pythagoras.
It is required to you
- - sheet of paper;
- - compasses;
- - ruler.
Instruction
1. Learn to use the rule of golden ratio at division of a piece. The golden ratio means its division into two unequal parts in a certain proportion for a piece. A smaller part so belongs to bigger as big to all length. Having designated piece length as L, its the most and smaller part, respectively, as an and b, you receive b ratio: and = and: L. Division of a piece is carried out by means of a ruler and compasses.
2. Draw a piece of any length. For convenience arrange it horizontally. Designate its final points as And yes V. Izmerte distance between them.
3. Divide piece length into 2. From a point In carry out to it a perpendicular. Lay off on it the distance equal to a half of length of an initial piece. Put S. Soyedinite's end this new point with A.U point you the rectangular triangle will turn out.
4. From a point With on a hypotenuse the EXPERT measure the piece equal to VS, and put the end of D. From a point And on direct AV postpone the size of this new piece and put the end E. It also divides an initial piece by the rule of golden ratio.
5. It is possible to find numerical value of this proportion. It is estimated on a formula h2-x-1=0. Find roots of this equation h1 and h2. Their values are equal to the sum or the difference of unit and a square root from five, divided into 2. That is h1=1+ √ 5)/2, and h2= (1-√ 5)/2. As a result the recurring irrational decimal turns out.
6. For practical application usually use an approximate ratio. Let's say that the whole piece of AV is equal to unit. Then the piece of AE will be approximately equal 0.62, and EV piece — 0.38.